Jika f(x)=x²-5x+1 dan (f o g)(x)=4x²+2x-5,maka g(3-4x)=

Jika f(x)=x²-5x+1 dan (f o g)(x)=4x²+2x-5,maka g(3-4x)=

$(fog)(x) = (4 {x}^{2} + 2x - 5)$

$f(g(x)) = (4 {x}^{2} + 2x - 5)$

$({g}^{2} (x) - 5.g(x) + 1) = (4 {x}^{2} + 2x - 5)$

$({g(x) - frac{5}{2} })^{2} - {( frac{5}{2}) }^{2} + 1 = (4 {x}^{2} + 2x - 5)$

${(g(x) - frac{5}{2} )}^{2} = (4 {x}^{2} + 2x - 5 + frac{5}{2} )$

$({g(x) - frac{5}{2} })^{2} = (4 {x}^{2} + 2x - frac{5}{2} )$

$g(x) - frac{5}{2} = sqrt{(4 {x}^{2} + 2x - frac{5}{2} ) }$

$g(x) = sqrt{(4 {x}^{2} + 2x - frac{5}{2} )} + frac{5}{2}$

Maka,

$g(3 - 4x) = sqrt{(4 {(3 - 4x)}^{2} + 2(3 - 4x) - frac{5}{2} )} + frac{5}{2}$

$g(3 - 4x) = sqrt{(4(9 - 12x - 12x + 16 {x}^{2} ) + 2(3 - 4x) - frac{5}{2} )} + frac{5}{2}$

$g(3 - 4x) = sqrt{(4(9 - 24x + 16 {x}^{2} ) + 2(3 - 4x) - frac{5}{2} )} + frac{5}{2}$

$g(3 - 4x) = sqrt{(36 - 96x + 64 {x}^{2} ) + (6 - 8x) - frac{5}{2} } + frac{5}{2}$

$g(3 - 4x) = sqrt{(64 {x}^{2} - 96x + 36 - 8x + 6 - frac{5}{2}) } + frac{5}{2}$

$g(3 - 4x) = sqrt{(64 {x}^{2} - 104x + 42 - frac{5}{2} )} + frac{5}{ 2}$

$g(3 - 4x) = sqrt{(64 {x}^{2} - 104x + 39 frac{1}{2}) } + frac{5}{2}$