Question

given f(x)=2x^2-4 and g(x)=5x+3
1. f(a)
2. f(3a)
3. f(a+b)
4. f(x+7)
5. f(5x+3)
6. g(f(x))

Answer 1

The function notation of f(x)=2x²-4 means that the letter "x" on each side of the equal sign takes on the same value. So
f(3) = 2(3)²-4 = 18-4 = 14
f(a) = 2(a)²-4 = 2a²-4
f(b+c) = 2(b+c)²-4 = 2b + 2c -4
etc.

since g(x)=5x+3,
f(g(x)) = f(5x+3) = 2(5x+3)² - 4
Expand the expression on the right hand side to get the final answer.