Test Index

MHTCET 19 Apr 2026 Shift 2 Paper

© examsnet.com

Question : 119 of 150

Marks: +1, -0

If

g(x)=1-\sqrt{x}

f(g(x))=5+4 \sqrt{x}+x

, then the value of

f(6)

is...

5
10
15
20

Solution:

Concept:

Replace

\sqrt{x}

using the definition of

g(x)

to express

f

in terms of a new variable.

Explanation:

Let

g(x) = 1 - \sqrt{x} = y

.

Then

\sqrt{x} = 1 - y

, so

x = (1-y)^2

.

Substitute these into

f(g(x)) = 5 + 4\sqrt{x} + x

.

f(y) = 5 + 4(1-y) + (1-y)^2

Expand and simplify:

f(y) = 5 + 4 - 4y + 1 - 2y + y^2

f(y) = y^2 - 6y + 10

Now substitute

y = 6

:

f(6) = 6^2 - 6(6) + 10 = 36 - 36 + 10 = 10

Answer:

f(6) = 10

, so the correct option is B.

© examsnet.com

Go to Question:

Prev Question

Next Question