For all 5 problems in this assignment, use the following functions: f(x) = x + 5
g(x) = x2 4x + 5
h(x) = 3x2 - 2x + 5
Match the function with its value.
(f+g)(x)
Choose...
(f*h)(x)
Choose...
h[f(5)] -g[h(1)] Choose...

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

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

b. x + 1

step-by-step explanation:

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