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Let f(x) =sinxandg(x)=x^(3) fog(x)....

Let f(x) `=sinxandg(x)=x^(3)`
`fog(x)`______.

A

`sinx^(3)`

B

`sin^(3)x`

C

`sin3x`

D

`3sinx`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the composition of the functions \( f(x) \) and \( g(x) \). Given: - \( f(x) = \sin x \) - \( g(x) = x^3 \) We want to find \( f(g(x)) \). ### Step-by-step Solution: 1. **Identify the functions**: We have two functions: - \( f(x) = \sin x \) - \( g(x) = x^3 \) 2. **Substitute \( g(x) \) into \( f(x) \)**: We need to find \( f(g(x)) \). This means we will replace \( x \) in \( f(x) \) with \( g(x) \). \[ f(g(x)) = f(x^3) \] 3. **Evaluate \( f(x^3) \)**: Now, we substitute \( x^3 \) into the function \( f(x) \): \[ f(x^3) = \sin(x^3) \] 4. **Write the final result**: Thus, we have: \[ f(g(x)) = \sin(x^3) \] ### Final Answer: \[ f(g(x)) = \sin(x^3) \] ---
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