Let f be the function defined by f\left(x\right)=3x^2+2x-4 and let g be the function defined by g\left(x\right)=3-2x.
Determine \left(g \circ f\right)\left(x\right).
If f and g are two functions, then the composition of these functions g\circ f is:
\left(g\circ f\right)\left(x\right)=g\left(f\left(x\right)\right)
Here:
\left(g\circ f\right)\left(x\right)=g\left(f\left(x\right)\right)=3-2\cdot f\left(x\right)=3-2\left(3x^{2}+2x-4\right)=3-6x^{2}-4x+8=-6x^{2}-4x+11
\left(g \circ f\right)\left(x\right)=-6x^2-4x+11
Let f be the function defined by f\left(x\right)=2\sqrt{x^{2}+5x-6} and let g be the function defined by g\left(x\right)=3x-2.
Determine \left(f \circ g\right)\left(x\right).
If f and g are two functions, then the composition of these functions f\circ g is:
\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)
Here:
\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)
\left(f\circ g\right)\left(x\right)=2\sqrt{\left(g\left(x\right)\right)^{2}+5 g\left(x\right)-6}
\left(f\circ g\right)\left(x\right)=2\sqrt{\left(3x-2\right)^{2}+5\left(3x-2\right)-6}
\left(f\circ g\right)\left(x\right)=2\sqrt{9x^{2}-12x+4+15x-10-6}
\left(f\circ g\right)\left(x\right)=2\sqrt{9x^{2}+3x-12}
\left(f\circ g\right)\left(x\right)=2\sqrt{9x^{2}+3x-12}
Let f be the function defined by f\left(x\right)=\dfrac{x-3}{x+1} and let g be the function defined by g\left(x\right)=\dfrac{2x+5}{x-6}.
Determine \left(f \circ g\right)\left(x\right).
If f and g are two functions, then the composition of these functions f\circ g is:
\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)
Here:
\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)=\dfrac{g\left(x\right)-3}{g\left(x\right)+1}=\dfrac{\dfrac{2x+5}{x-6}-3}{\dfrac{2x+5}{x-6}+1}=\dfrac{-x+23}{3x-1}
\left(f\circ g\right)\left(x\right)=\dfrac{-x+23}{3x-1}
Let f be the function defined by f\left(x\right)=4x^{2}-5x+6 and let g be the function defined by g\left(x\right)=x+2.
Determine \left(f \circ g\right)\left(x\right).
If f and g are two functions, then the composition of these functions f\circ g is:
\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)
Here:
\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)=4\left(g\left(x\right)\right)^{2}-5 g\left(x\right)+6
\left(f\circ g\right)\left(x\right)=4\left(x+2\right)^{2}-5\left(x+2\right)+6
\left(f\circ g\right)\left(x\right)=4\left(x^{2}+4x+4\right)-5x-10+6=4x^{2}+11x+12
\left(f\circ g\right)\left(x\right)=4x^{2}+11x+12
Let f be the function defined by f\left(x\right)=2x+1 and let g be the function defined by g\left(x\right)=x^{3}+4x+1.
Determine \left(g \circ f\right)\left(x\right).
If f and g are two functions, then the composition of these functions g\circ f is:
\left(g\circ f\right)\left(x\right)=g\left(f\left(x\right)\right)
Here:
\left(g\circ f\right)\left(x\right)=g\left(f\left(x\right)\right)=\left(f\left(x\right)\right)^{3}+4f\left(x\right)+1
\left(g\circ f\right)\left(x\right)=\left(2x+1\right)^{3}+4\left(2x+1\right)+1
\left(g\circ f\right)\left(x\right)=8x^{3}+12x^{2}+6x+1+8x+4+1
\left(g\circ f\right)\left(x\right)=8x^{3}+12x^{2}+14x+6
\left(g\circ f\right)\left(x\right)=8x^{3}+12x^{2}+14x+6
Let f be the function defined by f\left(x\right)=\ln\left(x\right) and let g be the function defined by g\left(x\right)=e^{2x}+3e^{x}+4.
Determine \left(g \circ f\right)\left(x\right).
If f and g are two functions, then the composition of these functions g\circ f is:
\left(g\circ f\right)\left(x\right)=g\left(f\left(x\right)\right)
Here:
\left(g\circ f\right)\left(x\right)=g\left(f\left(x\right)\right)=e^{2f\left(x\right)}+3e^{f\left(x\right)}+4=e^{2\ln\left(x\right)}+3e^{\ln\left(x\right)}+4=x^{2}+3x+4
\left(g\circ f\right)\left(x\right)=x^{2}+3x+4
Let f be the function defined by f\left(x\right)=\dfrac{2x+7}{3x-5} and let g be the function defined by g\left(x\right)=9x-1.
Determine \left(f \circ g\right)\left(x\right).
If f and g are two functions, then the composition of these functions f\circ g is:
\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)
Here:
\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)=\dfrac{2 g\left(x\right)+7}{3 g\left(x\right)-5}=\dfrac{2\left(9x-1\right)+7}{3\left(9x-1\right)-5}=\dfrac{18x+5}{27x-8}
\left(f\circ g\right)\left(x\right)=\dfrac{18x+5}{27x-8}