Question: Computers & Technology

How do i find the (gof)(x) and (fog)(x) for f(x)=x^2-11x, g(x)=2x+3? AND f(x)=1/x^2, g(x)= the square root of (x-1)?

In Computers & Technology | Asked by sathees2
Answers

(g o f)(x)
g(f(x)) (substitute x^2 - 11x for f(x))
g(x^2 - 11x) (substitute x^2 - 11x for x in g(x))
2(x^2 - 11x) + 3 (distribute)
2x^2 - 22x + 3 <===

(f o g)(x)
f(g(x)) (substitute 2x + 3 for g(x))
f(2x + 3) (substitute 2x + 3 for x in f(x))
(2x + 3)^2 - 11(2x + 3) (FOIL and distribute)
4x^2 + 12x + 9 - 22x - 33 (combine like terms)
4x^2 - 10x - 24 <===

(g o f)(x)
g(f(x)) (substitute 1/x^2 for f(x))
g(1/x^2) (substitute 1/x^2 for x in g(x))
√(1/x^2 - 1) (rewrite 1 as x^2/x^2)
√(1/x^2 - x^2/x^2) (subtract numerators)
√((1 - x^2)/x^2) (take the square root of the denominator x^2)
√(1 - x^2)/x <===

(f o g)(x)
f(g(x)) (substitute √(x - 1) for g(x))
f(√(x - 1)) (substitute √(x - 1) for x in f(x))
1/(√(x - 1)^2) (square the denominator)
1/(x - 1) <===

bhuvaneswari | 1542 days ago