If-g-x-4cos-4-x-2cos-2x-1-2-cos-4x-x-7-1-7-then-tbe-value-of-g-g-100-is-equal-to-

Question Number 143959 by bobhans last updated on 20/Jun/21

If g (x) = {(4 \cos^{4} x - 2 \cos 2 x - \frac{1}{2} \cos 4 x - x^{7})}^{\frac{1}{7}}

then tbe value of g (g (100)) is

equal to \dots

Answered by Olaf_Thorendsen last updated on 20/Jun/21

X = {4 \cos}^{4} x - 2 \cos 2 x - \frac{1}{2} \cos 4 x

X = 4 {(\frac{1 + \cos 2 x}{2})}^{2} - 2 \cos 2 x - \frac{1}{2} ({2 \cos}^{2} 2 x - 1)

X = \frac{3}{2}

g (x) = {(X - x^{7})}^{\frac{1}{7}}

g (x) = {(\frac{3}{2} - x^{7})}^{\frac{1}{7}}

g (100) = {(\frac{3}{2} - 100^{7})}^{\frac{1}{7}}

g o g (100) = {(\frac{3}{2} - g {(100)}^{7})}^{\frac{1}{7}}

g o g (100) = {(\frac{3}{2} - (\frac{3}{2} - 100^{7}))}^{\frac{1}{7}}

g o g (100) = 100