If f (x) = (20 – x^4)^(1/4) for 0 < x < √5, then f(f(1/2)) is equal to

Question

If f (x) = (20 – x⁴)^1/4 for 0 < x < \(\sqrt{5}\) , then \(f\big(f\big(\frac{1}{2}\big)\big)\) is equal to

(a) 2 ^{– 4} 

(b) 2 ^{– 3} 

(c) 2 ^{– 2} 

(d) 2 ^{– 1}

Answer 1

Answer: (d) 2 ^–1

f (x) = \((20-x^4)^{\frac{1}{4}}\) 

∴ \(f\big(\frac{1}{2}\big) \) = \((20-\frac{1}{16})^{\frac{1}{4}} = \big( \frac{319}{16}\big)^{\frac{1}{4}}\)

= \(\big(20-\frac{319}{16}\big)^{\frac{1}{4}}\)

= \((\frac{1}{16})^{\frac{1}{4}}\) = \(\frac{1}{2}\) 

= 2^-1