Composition and Inverses of Functions

Given  $f\left(x\right)=4x^2-5x+7$  and  $g\left(x\right)=3x^2-8x-9$  , find  $\left(f-g\right)\left(x\right)$  .

•  $7x^2-13x-2$  

•  $x^2-13x-2$  

•  $x^2+3x+16$  

•  $x^2+3x-2$  

Given $f\left(x\right)=x^2+x-56$ and $g\left(x\right)=x-7$ , find $\left(\frac{f}{g}\right)\left(x\right)$ .

• $x+8$ when $\left\{x\ne7\right\}$

• $x^2+8$ when $\left\{x\ne7\right\}$

• $x^2+2x+8$ when $\left\{x\ne7\right\}$

• $x+8$

Given  $f\left(x\right)=2x-5$  and  $g\left(x\right)=x^2-3x+8$  , find  $\left(f\circ g\right)\left(x\right)$  

•  $x^2-x+3$  

•  $2x^3-11x^2+31x-40$  

•  $2x^2-3x+3$  

•  $2x^2-6x+11$  

Given  $f\left(x\right)=x-6$  and  $g\left(x\right)=2x^2-5x+10$  , find  $\left(g\circ f\right)\left(x\right)$  

•  $2x^2-29x+112$  

•  $2x^2-5x-32$  

•  $2x^2-4x+4$  

•  $2x^3-17x^2+40x-60$  

Given  $f\left(x\right)=4x+3$  and  $g\left(x\right)=x^2-7x+10$  , find  $\left(f\circ f\right)\left(x\right)$  

•  $x^2-3x+13$  

•  $4x^2-28x+43$  

•  $16x+6$  

•  $16x+15$  

Find the inverse of the function  $f\left(x\right)=5x-7$  

•  $f^{-1}\left(x\right)=\frac{1}{5}x+\frac{7}{5}$  

•  $f^{-1}\left(x\right)=\frac{1}{5}x-\frac{7}{5}$  

•  $f^{-1}\left(x\right)=7x+5$  

•  $f^{-1}\left(x\right)=\frac{1}{5}x-\frac{1}{7}$  

Find the inverse of the function  $g\left(x\right)=x^2+3$  

•  $g^{-1}\left(x\right)=\frac{1}{2}x-\frac{3}{2}$  

•  $g^{-1}\left(x\right)=\pm\sqrt{x-3}$  

•  $g^{-1}\left(x\right)=\pm\sqrt{x}-3$  

•  $g^{-1}\left(x\right)=x^2-3$  

Given the function represented by the table, identify the function that is the inverse.

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Identify all pairs of inverse functions from their graphs.

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Identify the sets of inverse functions by using their result from composition of the functions.

• $f\left(g\left(x\right)\right)=2x-1$

• $f\left(g\left(x\right)\right)=x$

• $f\left(g\left(x\right)\right)=\frac{1}{3}x-3$

• $f\left(g\left(x\right)\right)=x^2-2$