91影视

The given functions are

$$\begin{gathered} f\left(x\right)=3x^3+1 \\ g\left(x\right)=2x^2-3 \end{gathered}$$.

We have to find $(f鈭�g)(-2).$

The definition of $(f鈭�g)\left(x\right)$is $f\left(g\right(x\left)\right).$

So,$(f鈭�g)(-2)=f\left(g\right(-2\left)\right).$

To find $f\left(g\right(-2\left)\right)$, put$-2$ in g(x).

Thus,

$$\begin{gathered} f\left(g\right(-2\left)\right)=f[2{(-2)}^2-3] \\ f\left(g\right(-2\left)\right)=f\left(5\right) \end{gathered}$$

By simplifying we get,

$$\begin{gathered} (f鈭�g)(-2)=f\left(g\right(-2\left)\right) \\ f\left(g\right(-2\left)\right)=f\left(5\right) \\ f\left(g\right(-2\left)\right)=3{\left(5\right)}^3+1 \\ f\left(g\right(-2\left)\right)=376 \\ (f鈭�g)(-2)=376 \end{gathered}$$

The given functions are

$$\begin{gathered} f\left(x\right)=3x^3+1 \\ g\left(x\right)=2x^2-3 \end{gathered}$$

We have to find $(g鈭�f)(-1).$

The definition of $(g鈭�f)\left(x\right)$is$g\left(f\right(x\left)\right).$

So,$(g鈭�f)(-1)=g\left(f\right(-1\left)\right).$

To find $g\left(f\right(-1\left)\right)$put$-1$ in f(x).

Thus,

$$\begin{gathered} g\left(f\right(-1\left)\right)=g[3{(-1)}^3+1] \\ g\left(f\right(-1\left)\right)=g(-2) \end{gathered}$$

By simplifying we get,

$$\begin{gathered} (g鈭�f)(-1)=g\left(f\right(-1\left)\right) \\ g\left(f\right(-1\left)\right)=g\left(2\right) \\ g\left(f\right(2\left)\right)=2{\left(2\right)}^2-3 \\ g\left(f\right(2\left)\right)=5 \\ (g鈭�f)\left(2\right)=5 \end{gathered}$$

The given functions are

$$\begin{gathered} f\left(x\right)=3x^3+1 \\ g\left(x\right)=2x^2-3 \end{gathered}$$

We have to find $(g鈭�g)\left(1\right).$

The definition of $(g鈭�g)\left(x\right)$is$g\left(g\right(x\left)\right).$

So, $(g鈭�g)\left(1\right)=g\left(g\right(1\left)\right).$

To find $g\left(g\right(1\left)\right)$put $1$in g(x).

Thus,

$$\begin{gathered} (g鈭�g)\left(1\right)=g\left(g\right(1\left)\right) \\ g\left(g\right(1\left)\right)=g[2{\left(1\right)}^2-3] \\ g\left(g\right(1\left)\right)=g(-1) \end{gathered}$$

By simplifying we get,

$$\begin{gathered} (g鈭�g)\left(1\right)=g\left(g\right(1\left)\right) \\ g\left(g\right(1\left)\right)=g(-1) \\ g\left(g\right(1\left)\right)=2{(-1)}^2-3 \\ g\left(g\right(1\left)\right)=-1 \\ (g鈭�g)\left(1\right)=-1 \end{gathered}$$