Function Inverses

Function Inverses

​How do I find the equation of an inverse function?

MGSE9-12.F.BF.4 Find Inverse Functions

Multiple Choice

Given the functions

$$f\left(x\right)=x^2+5$$  and  $$g\left(x\right)=4x-9$$   find  $$f-g$$  

• $$x^2+4x-4$$  

• $$4x^3-9x^2+20x-45$$  

• $$x^2-4x+14$$   

• $$-x^2+4x-14$$  

Multiple Choice

Given the functions

$$f\left(x\right)=x^2+5$$  and  $$g\left(x\right)=4x-9$$   find  $$f\times g$$  

• $$x^2+4x-4$$  

• $$4x^3-9x^2+20x-45$$  

• $$x^2-4x+14$$   

• $$-x^2+4x-14$$  

Multiple Choice

Given the functions

$$f\left(x\right)=x^2-3$$  and  $$g\left(x\right)=\sqrt{x-5}$$   find  $$g\circ f$$  

• $$\sqrt{x^2-8}$$  

• $$x-8$$  

• $$\sqrt{x^2+2}$$  

• $$x-2$$  

Fill in the Blanks

If $h\left(n\right)=-3n-5$   find $\left(h\ \circ\ h\right)\left(6\right)$  

Function Inverses

​How do I find the equation of an inverse function?

​Find g^-1(x).

​Find the inverse of h(x).

Multiple Choice

Find the inverse function.

$$h\left(x\right)=-x-3$$  

• $$h^{-1}\left(x\right)=-2x$$  

• $$h^{-1}\left(x\right)=2x-6$$  

• $$h^{-1}\left(x\right)=x+2$$  

• $$h^{-1}\left(x\right)=-x-3$$  

Multiple Choice

Find the inverse function.

$$g\left(x\right)=7x+3$$  

• $$g^{-1}\left(x\right)=-2x-6$$  

• $$g^{-1}\left(x\right)=2x-3$$  

• $$g^{-1}\left(x\right)=\frac{x-3}{7}$$  

• $$g^{-1}\left(x\right)=\frac{x+7}{3}$$  

Multiple Choice

Find the inverse function.

$$h\left(n\right)=\frac{n+5}{2}$$  

• $$h^{-1}\left(n\right)=-2n+1$$  

• $$h^{-1}\left(n\right)=2n-5$$  

• $$h^{-1}\left(n\right)=-3n+1$$  

• $$h^{-1}\left(n\right)=-\frac{5}{3}n$$  

Multiple Choice

Find the inverse. $$f\left(x\right)=-3x+1$$  

• $$f^{-1}\left(x\right)=\frac{5x+20}{3}$$  

• $$f^{-1}\left(x\right)=\frac{3x-9}{8}$$  

• $$f^{-1}\left(x\right)=\frac{x-5}{2}$$  

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

Multiple Choice

Find the inverse. $$g\left(n\right)=-2n-2$$  

• $$g^{-1}\left(n\right)=n-4$$  

• $$g^{-1}\left(n\right)=-2n-4$$  

• $$g^{-1}\left(n\right)=-n-2$$  

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