Q. 1 E4.0( 4 Votes )

Find gof and fog when f: R → R and g: R → R is defined byf(x) = x2 + 2x – 3 and g(x) = 3x – 4

Since, f:R R and g:R R

fog:R R and gof:R R

f(x) = x2 + 2x – 3 and g(x) = 3x – 4

Now, gof(x)=g(f(x))= g(x2 + 2x – 3)

gof(x) = 3(x2 + 2x–3) – 4

gof(x)= 3x2 + 6x – 9 – 4

gof(x) = 3x2 + 6x – 13

and, fog= f(g(x)) = f(3x – 4)

fog(x) = (3x – 4)2 + 2(3x – 4) – 3

= 9x2 + 16 – 24x + 6x – 8 – 3

fog(x) = 9x2 – 18x + 5

Thus, gof(x) = 3x2 + 6x – 13 and fog(x) = 9x2 – 18x + 5

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