Use f(x) = 2x + 5 and g(x) = x^2-1 to determine the following( simplified where possible):
(g * f)(3)
(g*f)(3)
= g(3) * f(3)
= (3^2-1)*(2*3+5)
= ...
So for (g*f)(3) the answer is 88, right. I have two other:
(f + g)(2), the answer would be 12, right and
for last qs: f(g(x)), I got 2x^3 + 5x^2 - 2x -5
Could you please clarify steve if these qs are right.
Thanks
f(x) = 2x + 5 and g(x) = x^2-1
the f(g(x))
= f(x^2 - 1)
= 2(x^2 - 1) + 5
f(g(x)) = 2x^2 - 2 + 5 = 2x^2 + 3
check: try x = 6
g(6) = 36-1 = 35
f(35) = 2(35) + 5 = 75
in my answer of
f(g(x)) = 2x^2 + 3
f(g(6)) = 2(36) + 3 = 75
you did (f*g)(x), not (f◦g)(x) = f(g(x))
To find (g * f)(3), we need to first determine the compositions of the functions g(x) and f(x) individually, and then evaluate the resulting expression at x = 3.
Starting with g(x) = x^2 - 1, we substitute f(x) into the equation for x. This gives us:
g(f(x)) = (f(x))^2 - 1
Now, substituting f(x) = 2x + 5 into the equation, we get:
g(2x + 5) = (2x + 5)^2 - 1
Expanding this expression, we have:
g(2x + 5) = (2x + 5)(2x + 5) - 1
= 4x^2 + 10x + 10x + 25 - 1
= 4x^2 + 20x + 24
Finally, to find (g * f)(3), we substitute x = 3 into this expression:
(g * f)(3) = 4(3)^2 + 20(3) + 24
= 4(9) + 60 + 24
= 36 + 60 + 24
= 120 + 24
= 144
Therefore, (g * f)(3) equals 144.