Question

F(x)=√x
G(x)=x²-1
Para ahorita es urgente

Answer 1

Letf:A→Bandg:B→Abetwogivenfunctions

\sf{Then \: the \: function \: gof : B \to \: B \: is \: defined \: as}Thenthefunctiongof:B→Bisdefinedas

\sf{ \: (gof)(x) = g(f(x))\: }(gof)(x)=g(f(x))

GIVEN

\sf{ f(x) = {x}^{2} - 1 \: }f(x)=x2−1

\sf { \: g(x) = {(x + 1)}^{2} \: }g(x)=(x+1)2

TO DETERMINE

\sf{ \: (gof)(x) \: }(gof)(x)

CALCULATION

\sf{ \: (gof)(x) \: }(gof)(x)

\sf{ = g(f(x))\: }=g(f(x))

\sf{ \: = g( {x}^{2} - 1)\: }=g(x2−1)

\sf{ \: = {( {x}^{2} - 1 + 1) }^{2} \: }=(x2−1+1)2

= \sf{{( {x}^{2} )}^{2} }=(x2)2

= \sf{ \: {x}^{4} }=x4

Hence

\sf{ \: (gof)(x) = {x}^{4} \: }(gof)(x)=x4

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LEARN MORE FROM BRAINLY

Let A={1,2,0,-1} B={1,3-1,-3} and

function f = A to B f(x) =px+q

If f={ (1,1),(2,3),(0,-1),(-1,-3)}