1.Given f(x)-2x-11 find f^1(x)

2.Describe the transformation of the parent function f(x) h(x)=-3f(x)

3.Let f(x)=x^2+7x+9. does an inverse function exist for the entire domain of the function? Explain.

Guest May 12, 2020

#1**+1 **

1. We can write

y = -2x -11 get x by itself

y +11 = - 2x

[ y +11] / -2 = x

- [ y +11] / 2 = x "swap" x and y

- [x + 11] / 2 = y = f^{-1}(x)

2. h(x) vertically "stretches" f(x) by a factor of 3 and the "-" flips this over the x axis

See the graph here : https://www.desmos.com/calculator/9fq01ty1j3

3. This has an inverse but it will not be a function......

f(x) = x^2 + 7x + 9 is a parabola that turns upward.......thus.....it will not pass the horizontal line test [ a horizontal line drrawn through the function will cut the function in more than one place......so....not one-to-one ]

So....if the original function is not one-to-one , then it won't have an inverse over its entire domain

CPhill May 12, 2020