If f(x)=x+2, g(x)=7^x, then go f(x)=

Option c: 49(7^x). Solution: To find the composite function (g circ f)(x) = g(f(x)), we substitute f(x) into g(x): Given: f(x) = x + 2 g(x) = 7^x Substitute f(x) in place of x in g(x): g(f(x)) = 7^{f(x)} = 7^{x + 2} Using the algebraic exponent rule a^{m+n} = a^m a^n, we can rewrite this as: 7^{x + 2} = 7^x 7^2 = 7^x 49 = 49(7^x) Hence, Option C is the correct answer.

If $f(x)=x+2, g(x)=7^x$, then $go f(x)=$

The correct answer is Option c: $49(7^x)$. To find the composite function $(g \circ f)(x) = g(f(x))$, we substitute $f(x)$ into $g(x)$: Given: $$f(x) = x + 2$$ $$g(x) = 7^x$$ Substitute $f(x)$ in place of $x$ in $g(x)$: $$g(f(x)) = 7^{f(x)} = 7^{x + 2}$$ Using the algebraic exponent rule $a^{m+n} = a^m \cdot a^n$, we can rewrite this as: $$7^{x + 2} = 7^x \cdot 7^2 = 7^x \cdot 49 = 49(7^x)$$ Hence, **Option C** is the correct answer.

Set, Relations and FunctionsMTP Dec 2023 Series IQuestion 2000 of 217

All Questions

If $\displaystyle f(x)=x+2, g(x)=7^x$ , then $\displaystyle go f(x)=$

Options

\displaystyle 7^x.x+2.7^x

\displaystyle 7^x+2

\displaystyle 49(7^x)

DNone of these

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Correct Answer

✅ Option c — $\displaystyle 49(7^x)$

All Options:

A $\displaystyle 7^x.x+2.7^x$
B $\displaystyle 7^x+2$
C $\displaystyle 49(7^x)$
DNone of these

Detailed Solution & Explanation

To find the composite function

\displaystyle (g \circ f)(x) = g(f(x))

, we substitute

\displaystyle f(x)

into

\displaystyle g(x)

:
Given:

f(x) = x + 2

g(x) = 7^x

Substitute

\displaystyle f(x)

in place of

\displaystyle x

\displaystyle g(x)

g(f(x)) = 7^{f(x)} = 7^{x + 2}

Using the algebraic exponent rule

\displaystyle a^{m+n} = a^m \cdot a^n

, we can rewrite this as:

7^{x + 2} = 7^x \cdot 7^2 = 7^x \cdot 49 = 49(7^x)

Hence, **Option C** is the correct answer.

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If f(x)=x+2,g(x)=7x\displaystyle f(x)=x+2, g(x)=7^xf(x)=x+2,g(x)=7x, then gof(x)=\displaystyle go f(x)=gof(x)=