FNGR 2 | Lesson 5 | Try This! (Writing Inverse Equations)

Writing Inverse Equations

Part 1:  Use composition to determine if $$f$$ and $$g$$ are inverse functions.

1.  $$f(x)=2x^2-1$$  and  $$g(x)=x-1$$ , find $$f(g(x))$$ .

2.  $$f(x)=2x-1$$  and  $$g(x)=\dfrac{x+1}{2}$$ , find $$f(g(x))$$ and $$g(f(x))$$ .

Part 2:  Determine which of the following functions have an inverse (pass the horizontal line test).  If the function has an inverse, write its equation.

3.  $$f(x) = 3x-1$$

4.  $$f(x) = \dfrac 4x$$

5.  $$f(x) = 3x^2+2$$

6.  $$f(x) = x^3+1$$