If f:R→R is given by f(x)=(5+x4)1/4, then fοf(x) is

The correct option is (10+x⁴)¹/⁴.

Step-by-step Explanation:

We are given the function:
$$f\left(x\right)={(5+x^4)}^{1/4}$$

We want to find the composite function $(f\circ f)\left(x\right)$, which is defined as:
$$(f\circ f)\left(x\right)=f\left(f\right(x\left)\right)$$

Substitute the expression for $f\left(x\right)$ into itself:
$$f\left(f\right(x\left)\right)={[5+{\left(f\right(x\left)\right)}^4]}^{1/4}$$

Now, substitute $f\left(x\right)={(5+x^4)}^{1/4}$ into the equation:
$$f\left(f\right(x\left)\right)={[5+{\left({(5+x^4)}^{1/4}\right)}^4]}^{1/4}$$

Simplify the inner term. Since ${\left(a^m\right)}^n=a^{m\cdot n}$, we have:
$${[{(5+x^4)}^{1/4}]}^4={(5+x^4)}^{\frac{1}{4}\cdot 4}=5+x^4$$

Substitute this simplified term back into the expression:
$$f\left(f\right(x\left)\right)={[5+(5+x^4\left)\right]}^{1/4}$$

Combine the constant terms inside the bracket:
$$f\left(f\right(x\left)\right)={(10+x^4)}^{1/4}$$

Thus, the value of $(f\circ f)\left(x\right)$ is ${(10+x^4)}^{1/4}$.