let f(x)= 4x+4, g(x) =x4. Find f(x)g= g(x)f= let f(x) =√x2+5,g(x)=x2 +3.Find f(x)g= g(x)f=

Question

let f(x)= 4x+4, g(x) =x⁴. Find

f(x)g= g(x)f=

let f(x) =√x²+5,g(x)=x² +3.Find

f(x)g= g(x)f=

Answer 1

This looks like a function composition problem, although the way that it is written is not quite correct.

By f(x)g and g(x)f, I assume that you mean f(g(x)) and g(f(x)). This could also be written as f ∘ g and g ∘ f in most textbooks. Here is how you can solve a problem like this one.

Let f(x) = 4x + 4 g(x) = x⁴

Then f ∘ g = f(g(x)) = f(x⁴) = 4x⁴ + 4

and g ∘ f = g(f(x)) = g(4x + 4) = (4x + 4)⁴

Let f(x) = √(x²+5) g(x) = x² + 3

Then f ∘ g = f(g(x)) = √((x² + 3)²+5)

If necessary, you could expand this out to simplify slightly more

√((x² + 3)²+5) = √(x⁴ + 6x² + 9 + 5) = √(x⁴ + 6x² + 14)



and g ∘ f = g(f(x)) = x² + 3 = (√(x²+5))² + 3 = x² + 5 + 3 = x² + 8