Compose two functions - High school Precalculus Exercises

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).

\left(g \circ f\right)\left(x\right)=-6x^2-4x+11

\left(g \circ f\right)\left(x\right)=12x² - 40x + 29

\left(g \circ f\right)\left(x\right)=12x² - 4x + 29

\left(g \circ f\right)\left(x\right)=-6x^2+4x-5

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).

\left(f\circ g\right)\left(x\right)=2\sqrt{9x^{2}+15x-12}

\left(f\circ g\right)\left(x\right)=6\sqrt{x^{2}+5x-6}-2

\left(f\circ g\right)\left(x\right)=2\sqrt{9x^{2}+3x-12}

\left(f\circ g\right)\left(x\right)=2\sqrt{3x^{2}+15x-20}

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).

\left(f\circ g\right)\left(x\right)=\dfrac{x+1}{x+3}

\left(f\circ g\right)\left(x\right)=\dfrac{-x+23}{3x-1}

\left(f\circ g\right)\left(x\right)=\dfrac{7x-1}{-5x-9}

\left(f\circ g\right)\left(x\right)=\dfrac{-x-13}{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).

\left(f\circ g\right)\left(x\right)=4x^{2}+11x+12

\left(f\circ g\right)\left(x\right)=4x^{2}-5x+12

\left(f\circ g\right)\left(x\right)=16x^{2}+61x+60

\left(f\circ g\right)\left(x\right)=4x^{2}-5x+8

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).

\left(g\circ f\right)\left(x\right)=8x^{3}+8x+6

\left(g\circ f\right)\left(x\right)=8x^{3}+6x^{2}+14x+6

\left(g\circ f\right)\left(x\right)=2x^{3}+8x+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).

\left(g\circ f\right)\left(x\right)=x^{2}+3x+4

\left(g\circ f\right)\left(x\right)=5x+4

\left(g\circ f\right)\left(x\right)=5\ln\left(x\right)+4

\left(g\circ f\right)\left(x\right)=\ln\left(x^{2}+3x+4\right)

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).

\left(f\circ g\right)\left(x\right)=\dfrac{18x+6}{27x-6}

\left(f\circ g\right)\left(x\right)=\dfrac{18x+5}{27x-8}

\left(f\circ g\right)\left(x\right)=\dfrac{15x+68}{3x-5}

\left(f\circ g\right)\left(x\right)=\dfrac{15x+58}{3x-5}