Cimposition of functionsss

Question

F(x)= 3-x, g(x)= x^2 h(x)= x+6. Find GoHoF

Answer 1

f(x) = 3 - x, g(x) = x² and h(x) = x + 6.

GoHoF(x) = g(h(f(x)))

g(h(f(x))) = g(h(3 - x))                                             f(x) = 3 - x.

= g(h(3 - x))

= g(3 - x + 6)                                                         h(x) = x + 6

= g(-x + 6)

= g(-x + 3)

= (3 - x)²                                                                 g(x) = x²

Mathematical formula: (a - b)²= a²+ b²- 2ab

= 3²+ x²- 2(3)(x)

= 9 + x²- 6x

= x²- 6x + 9.

Therefore GoHoF = x²- 6x + 9.

Comments

g oh of  = x ² + 81 - 18x.

Answer 2

The functions are f (x ) = 3 - x , g (x ) = x ² and h (x ) = x + 6

g oh of  = g oh of (x )

= g (h (f (x )))

Substitute the expression for functioning f  (in this case 3 - x ) for f (x ) in the composition.

= g (h (3 - x ))

Now substitute this expression (3 - x ) in to function h in place of the x  value.

= g (3 - x + 6)

= g(- x + 9)

Now substitute this expression (- x + 9) in to function g (in this case x ² ) in place of x  value.

= (- x + 9)²

= x ² + 81 -18x

g oh of  = x ² + 81 - 18x.