Question Type 2: Finding complex combination of composite functions given two or more functions Exercises

With $f(x)=5x^3+9$ and $g(x)=2x-1$, find the composite function $(f\,\circ\,g)(x)$.

Given the functions $f(x)=5x^3+9$ and $g(x)=2x-1$, calculate the composite function $(g\,\circ\,f)(x)$.

Given $f(x)=3x^2-4$ and $g(x)=\sqrt{x}$, find $(f\circ g)(x)$.

Let $f(x)=3x^2-4$ and $g(x)=\sqrt{x}$. Determine $(g\circ f)(x)$.

Let $f(x)=5x^3+9$ and $g(x)=x\,5^x\,e^x$. Compute the composite function $(g\circ f)(x)$.

For $f(x)=5x^3+9$ and $g(x)=x\,5^x\,e^x$, find the composite function $(f\circ g)(x)$.

Let $f(x)=\sin(x)$, $g(x)=x^2$ and $h(x)=\frac{1}{x+1}$. Determine $(h\circ g\circ f)(x)$.

With $g(x)=x^2+1$, $h(x)=e^x$ and $f(x)=\ln(x)$, find the composite $(h\circ f\circ g)(x)$.

Let $g(x)=x^2+1$, $h(x)=e^x$ and $f(x)=\ln(x)$. Determine the triple composite $(f\circ h\circ g)(x)$.

Given $f(x)=5x^3+9$, $g(x)=x\,5^x\,e^x$ and $h(x)=3g(x)f\bigl(g(x)\bigr)$, find the composite $(h\circ g)(x)$.

Let $f(x)=5x^3+9$, $g(x)=x\,5^x\,e^x$ and $h(x)=3g(x)f\bigl(g(x)\bigr)$. Determine $(h\circ f)(x)$.