Question

If f(x) = 3^x + 10x and g(x) = 4x – 2, find (f + g)(x).

A. 3^x + 6x + 2
B. 3^x + 14x – 2
C. 3^x – 6x + 2
D. 17x - 2

Answer 1

The correct option is B.
`(f+g)(x)=3^(x)+14x-2`

Explanation:

Consider the provided function:

`f(x)=3^(x)+10x` and
`g(x)=4x-2`

`(f+g)(x)` is saying we want to add
`f(x)`and
`g(x)`.

In order to find the value of
`(f+g)(x)` simply add them as shown below:

`(f+g)(x)=3^(x)+10x+4x-2`

`(f+g)(x)=3^(x)+14x-2`

Therefore, the correct option is B.
`(f+g)(x)=3^(x)+14x-2`

Answer 2

B. 3^x +14x -2

Explanation:

In general, the expression (f ⊛ g)(x) will mean the operation ⊛ will be performed on the values of the functions:

(f ⊛ g)(x) ≡ f(x) ⊛ g(x)

The exception is the "ring" or "composition" operator, which indicates the left function is performed on the right function:

(f ∘ g)(x) ≡ f(g(x))

The expression (f +g)(x) means the function values are added.

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function sum

For the functions here, we add them by combining like terms:

(f +g)(x) = f(x) +g(x)

= (3^x +10x) +(4x -2)

= 3^x +(10 +4)x - 2

= 3^x +14x -2 . . . . . . . . . corresponds to choice B