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. \(f(x) = x^3+1\)
Check your solutions here.
