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If
f(x)=e^(x//8),g(x)=6x+9, and
h(x)=sqrtx, Find a simplified formula for:
f(g(x))h(x)=

If $f(x)=e^{x / 8}, g(x)=6 x+9$ , and $h(x)=\sqrt{x}$ , Find a simplified formula for: $f(g(x)) h(x)=$

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Evaluate exponential functions

Full solution

Q. If

f(x)=e^{x / 8}, g(x)=6 x+9

, and

h(x)=\sqrt{x}

, Find a simplified formula for:

f(g(x)) h(x)=

Substitute $g(x)$ into $f(x)$ : Step $1$ : Substitute $g(x)$ into $f(x)$ . $\newline$ - Calculation: $f(g(x)) = e^{(g(x)/8)}$ $\newline$ - Substitute $g(x) = 6x + 9$ into the equation. $\newline$ - $f(g(x)) = e^{((6x + 9)/8)}$
Simplify expression inside exponent: Step $2$ : Simplify the expression inside the exponent. $\newline$ - Calculation: Simplify $(6x + 9)//8$ . $\newline$ - Since // denotes integer division, $(6x + 9)//8$ will simplify based on integer values. $\newline$ - For large values of $x$ , this simplifies to $6x//8 + 9//8$ . $\newline$ - $6x//8$ simplifies to $3x/4$ (incorrect simplification, should be $0.75x$ but integer division rounds down). $\newline$ - $9//8$ simplifies to $1$ . $\newline$ - Therefore, $f(g(x)) = e^{(0.75x + 1)}$ .

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