If f(x) = x-3 g(x) = 2x+5 find fog and gof
Do you mean
f(g(x)) and g(f(x)) ?
f(g(x)) = (2x+5)-3 = 2x + 2
g(f(x)) = 2(x-3) + 5 = 2x -1
how do you get the answer tho?
To find the composition of functions f o g, we substitute the expression of g(x) into f(x), where g(x) is the input of f(x). Similarly, to find the composition of functions g o f, we substitute the expression of f(x) into g(x), where f(x) is the input of g(x).
Let's find f o g:
fog(x) = f(g(x))
= f(2x+5) [Substitute the expression of g(x)]
= (2x+5) - 3 [Substitute the expression of f(x) into f(g(x))]
= 2x + 5 - 3
= 2x + 2
Therefore, fog(x) = 2x + 2.
Now, let's find g o f:
gof(x) = g(f(x))
= g(x-3) [Substitute the expression of f(x)]
= 2(x-3) + 5 [Substitute the expression of g(x) into g(f(x))]
= 2x - 6 + 5
= 2x - 1
Therefore, gof(x) = 2x - 1.
So, the compositions of functions f o g and g o f are fog(x) = 2x + 2 and gof(x) = 2x - 1, respectively.