# Let f(x) = 3x^{2} - x + 2 and g(x) = 5x^{2} - 1. Find f(g(x)). Show each step of your work.

**Solution:**

f(x) = 3x^{2} - x + 2

g(x) = 5x^{2} - 1

The composite function fog(x) = f [g(x)]

f [g(x)] = f [5x^{2} - 1]

The input for f(x) is the output of g(x).

f(x) = 3x^{2} - x + 2 in the above condition with replacement of 5x^{2} - 1 function in the place of x gives

f [5x^{2} - 1] = 3(5x^{2} - 1)^{ 2} - (5x^{2} - 1) + 2

f [g(x)] = 3(5x^{2} - 1)^{2} - (5x^{2} - 1) + 2 = 3(25x^{4} + 1 - 10x^{2}) - 5x^{2} + 1 + 2

f [g(x)] = 75x^{4} + 3 - 30x^{2} - 5x^{2} + 3

So f [g(x)] = 75x^{4} - 35x^{2} + 6

## Let f(x) = 3x^{2} - x + 2 and g(x) = 5x^{2} - 1. Find f(g(x)). Show each step of your work.

**Summary:**

If f(x) = 3x^{2} - x + 2 and g (x) = 5x^{2} - 1 then f (g(x)) = 75x^{4} - 35x^{2 }+ 6

Composite function is fog = f(g) if f: A to B and g: B to C then gof: A to C is a composite function from A to C.