1. ## Functions

If $\displaystyle f(x) = 4x + 3$and $\displaystyle h(x) = 8x^2 -1.$
a) Find x so that f(x) = h(x)
b) Find a function g(x) so that f(g(x)) = h(x)

can someone exaplin to me how to do this?

2. Originally Posted by foreverbrokenpromises
If $\displaystyle f(x) = 4x + 3$and $\displaystyle h(x) = 8x^2 -1.$
a) Find x so that f(x) = h(x)
b) Find a function g(x) so that f(g(x)) = h(x)

can someone exaplin to me how to do this?

Part a) Let f(x) = h(x) = y. Now solve $\displaystyle y = 4x + 3$ and $\displaystyle y = 8x^2 - 1$ simultaneously.

Part b) Since f(g(x)) means substitute every x value in f(x) with function g(x), basically it wants you to solve this:

$\displaystyle 4[g(x)] + 3 = 8x^2 - 1$
You need to find a function g(x) in terms of x to make the LHS = RHS.

3. a) solve $\displaystyle 4x + 3 = 8x^2 -1$. you should be able to do this

b) if $\displaystyle f(g(x)) = h(x)$ then $\displaystyle f^{-1}(f(g(x))) = f^{-1}(h(x))$ or $\displaystyle g(x) = f^{-1}(h(x))$

4. Originally Posted by Gusbob
Part a) Let f(x) = h(x) = y. Now solve $\displaystyle y = 4x + 3$ and $\displaystyle y = 8x^2 - 1$ simultaneously.

Part b) Since f(g(x)) means substitute every x value in f(x) with function g(x), basically it wants you to solve this:

$\displaystyle 4[g(x)] + 3 = 8x^2 - 1$
You need to find a function g(x) in terms of x to make the LHS = RHS.

for a) i got x = -1/2 or x =1