We are looking for two functions, [latex]g[/latex] and [latex]h[/latex], so [latex]f\left(x\right)=g\left(h\left(x\right)\right)[/latex]. To do this, we look for a function inside a function in the formula for [latex]f\left(x\right)[/latex]. As one possibility, we might notice that the expression [latex]5-{x}^{2}[/latex] is the inside of the square root. We could then decompose the function as

[latex]h\left(x\right)=5-{x}^{2}\hspace{2mm}\text{and}\hspace{2mm}g\left(x\right)=\sqrt{x}[/latex]

We can check our answer by recomposing the functions.

[latex]g\left(h\left(x\right)\right)=g\left(5-{x}^{2}\right)=\sqrt{5-{x}^{2}}[/latex]

We are looking for two functions, [latex]g[/latex] and [latex]h[/latex], so [latex]f\left(x\right)=g\left(h\left(x\right)\right)[/latex]. To do this, we look for a function inside a function in the formula for [latex]f\left(x\right)[/latex]. As one possibility, we might notice that the expression [latex]4x-3[/latex] is within the exponent of the exponential function. We could then decompose the function as

[latex]h\left(x\right)=4x-3\hspace{2mm}\text{and}\hspace{2mm}g\left(x\right)=e^{x}[/latex]

We can check our answer by recomposing the functions.

[latex]g\left(h\left(x\right)\right)=g(4x-3)=e^{4x-3}[/latex]