# Let f(x)=3x^{2}-x+2 and g(x)=5x^{2}-1. What is f(g(x))?

**Solution:**

g(x) = y\(_1\)_{ }= 5x^{2 }- 1 ….. (1)

f(x) = y\(_2\)= 3x^{2 }- x + 2 ….. (2)

f(g(x)) is a composite function and can be written as (fog)(x)

Where x is present in f(x) you should substitute y\(_1\)_{ }

I.e., substituting equation (1) in x which is present in equation (2)

f(g(x)) = 3 y\(_1\)_{ }^{2}_{ }- y\(_1\)_{ } + 2 where y_{1 }= 5x^{2 }- 1

f(g(x)) = 3 (5x^{2 }- 1)^{2}_{ }- (5x^{2 }- 1) + 2

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

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

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

Therefore, f(g(x)) is (75x^{4}_{ }- 35x^{2} + 6).

## Let f(x)=3x^{2}-x+2 and g(x)=5x^{2}-1. What is f(g(x))?

**Summary:**

Let f(x)=3x^{2}-x+2 and g(x)=5x^{2}-1. f(g(x)) is (75x^{4}_{ }- 35x^{2} + 6).