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.