Answer:
1.) x^2 + 3x
2.) 3x^2 - 3x
3.) 278
Step-by-step explanation:
You are given the following functions:
f(x) = x + 5
g(x) = x2 + 4x + 5
h(x) = 3x2 - 2x + 5
1.) To match the function with its value,
(f+g)(x) = f(x) + g(x)
Substitutes for the two functions
X + 5 = x^2 + 4x + 5
Collect the like terms and equate them to zero
X^2 + 4x - x + 5 - 5
X^2 + 3x
Therefore, (f+g) (x) = x^2 + 3x
2.) (f*h)(x) = f(x) × h(x)
x + 5 = 3x^2 - 2x + 5
Collect the like terms
3x^2 - 2x - x + 5 - 5
3x^2 - 3x
Therefore, (f×h)(x) = 3x^2 - 3x
3.) h[f(5)] -g[h(1)]
First find f(5)
That is, substitute x for 5 in f(x)
f(5) = 5 + 5 = 10
Also, do the same for h(1)
h(1) = 3(1)^2 - 2(1) + 5
h(1) = 3 - 2 + 5 = 6
h[f(5)] - g[h(1)]
= 3(10)^2 - 2(10) + 5 - (6)^2 + 4(6) + 5
= 300 - 20 + 5 - 36 + 24 + 5
= 334 - 56
= 278
Therefore, h[f(5)] - g[h(1)] = 278
