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Sets, Relations and Functions

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Question : 25 of 65

Marks: +1, -0

If

f(x)=2 x+5

g(x)=x^{2}+1

=?

$2 x^{2}+7$
$2 x+1$
$x^{2}+5$
None

Solution:

Concept:

Composition of functions

f(g(x))

substitutes

g(x)

into

f(x)

.

Explanation:

Given

f(x)=2x+5

and

g(x)=x^2+1

, we compute

fog = f(g(x))

.

Substitute

g(x)

into

f(x)

:

f(g(x)) = 2(g(x)) + 5 = 2(x^2+1) + 5

.

Simplify:

2(x^2+1) = 2x^2 + 2

, then add

5

to get

2x^2 + 7

.

Answer:

fog = 2x^{2} + 7

, which corresponds to option A.

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