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.
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