Mathematics - Indefinite Integration Question with Solution | TestHub

MathematicsIndefinite IntegrationMiscellaneous formMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

Let function $f : R \to R$ and $g : R \to R$ satisfy $f (x + g (y)) = 2 x + y + 5$ and $g (0) = 0$ .

The value of $g (x + f (y))$ when $x = 1$ and $y = 2$ is -

Answer:

Solution:

g(0) = 0

f(x) = 2x + 5

f(x + g(y)) = 2x + y + 5

f(0) = 5

f(g(x + f(y))] = 5 + x + f(y)

f[(g{(x) + f(y)}] = 5 = 5 + x + f(y)

2g(x + f(y)) = x + f(y)

at y = 2, f(2) = 9

2g(10) = 1 + 9 = 10

g(10) = 5

Stream:JEESubject:MathematicsTopic:Indefinite IntegrationSubtopic:Miscellaneous form

⏱ 2mℹ️ Source: QB

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