If f(x)=x³-x and g(x)= \;2x, then f≤ft(g≤ft(π/12)) =

Correct Answer is : −38-3/8−83

Correct Answer is : −38-3/8−83

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AP EAPCET 15th May 2023 Shift 1 Solved Paper

Section: Mathematics

Question : 1 of 160

Marks: +1, -0

f(x)=x^3-x

g(x)= \sin \;2x

f\left(g\left(\frac{\pi}{12}\right)\right) =

Solution: 👈: Video Solution

To solve the problem, we need to find the value of

f\left(g\left(\frac{\pi}{12}\right)\right)

where

f(x) = x^3 - x

and

g(x) = \sin(2x)

First, we need to find the value of

g\left(\frac{\pi}{12}\right)

g\left(\frac{\pi}{12}\right) = \sin\left(2 \cdot \frac{\pi}{12}\right) = \sin\left(\frac{\pi}{6}\right)

We know that

\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}

, so:

g\left(\frac{\pi}{12}\right) = \frac{1}{2}

Next, we need to find the value of

f\left(\frac{1}{2}\right)

f\left(\frac{1}{2}\right) = \left(\frac{1}{2}\right)^3 - \frac{1}{2} = \frac{1}{8} - \frac{1}{2} = \frac{1}{8} - \frac{4}{8} = -\frac{3}{8}

Therefore, the value of

f\left(g\left(\frac{\pi}{12}\right)\right)

is:

f\left(g\left(\frac{\pi}{12}\right)\right) = -\frac{3}{8}

The correct answer is:

-\frac{3}{8}

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