Question

if f(x)=2x^2+x-5, g(x)=2x-5, h(x)=x-2/1+x, find f^1(x)

Answer 1

Are you asked to find the inverse function of f(x) ?

Answer 2

yes

Answer 3

f(x)=2x^2+x-5
y = 2x^2 + x - 5
y = 2(x^2 + 1/2x - 5/2)
complete the square:
y = 2{ (x+1/4)^2 - 1/16 - 5/2 }
y / 2 = (x+1/4)^2 - 1/16 - 40/16 = (x+1/4)^2 - 41/16
y/2 + 41/16 = (x+1/4)^2
(8y + 41) / 16 = (x+1/4)^2
Take square root on both sides:
sqrt(8y+41) / 4 = x + 1/4
x = { sqrt(8y+41) - 1 } / 4
interchange x and y:
y = { sqrt(8x+41) - 1 } / 4

Answer 4

Thank you!!!:)

Answer 5

\[
f^{-1}(x) = \frac{\pm\sqrt{8x+41} - 1}{4}
\]

Answer 6

You are welcome.

Answer 7

What about h^-1(x)?

Answer 8

Is it the same steps?

Answer 9

To find the inverse of h(x):
1. Replace h(x) by y.
2. Solve for x in terms of y.
3. Interchange x and y
4. Replace y by h^(-1)(x)