Algebra Composition of Function Help?

Question

Need assistance with the following problem: if f(x) = 1 + x^2 and g(x) = sqrt (x-1) what is g o f and (f o g)(2)

Answer 1

g o f (x) = sqrt((1 + x^2) - 1) gof(2) = sqrt((1 + 2^2) -1) = sqrt(4) = 2
f o g(x) = 1 + (sqrt(x-1))^2 fog(2) = 1 + (sqrt(2-1))^2 = 1 + 1^2 = 2

Answer 2

I don't really understand what is g o f and (f o g)(2).
But I assume g o f is [gf(x)] and (f o g)(2) is [fg(2)].

f(x) = 1 + x^2 and g(x) = (x -1)²

[gf(x)]
= g(1 + x²)
= [(1 + x²) - 1]²
= 1² + 2x² + x^4 - 1²
= 2x² + x^4 (final answer)

If you want to find [gf(2)]
= 2x² + x^4
= 2(2)² + 2^4
= 8 + 16
= 24 (final answer)

f(x) = 1 + x² and g(x) = (x -1)²

[fg(x)]
= f(x -1)²
= 1 + [(x -1)²]²
= 1 + (x² - 2x + 1²)²
= 1 + x^4 - 2x² + 1^4
= x^4 - 2x² + 1

[fg(2)]
= x^4 - 2x² + 1
= 2^4 - 2(2)² + 1
= 16 - 8 + 1
= 9 (final answer)

Answer 3

First for f(g(x)), this suggests that as quickly as you come back throughout an "x" interior the f(x) equation, you plug interior the g(x) value. So the problem might appear as if 3(x^2) so the respond for f(g(x)) could be 3x^2. For g(f(x)) you do an identical ingredient; once you come back throughout an "x" in that equation, plug interior the cost this is f(x). So the equation might appear as if (3x)^2. So the respond for g(f(x)) is 9x^2.