Given fxx29 gx2x hxx3 Find the following 1 f3 2 g3 3 h6 4 fg

Given f(x)=x²-9, g(x)=2x, h(x)=x-3 Find the following 1.) f(3) 2.) g(3) 3.) h(6) 4.) (f+g)x 5.) (f+g) (3) 6.) (f-h)(-3) 7.) (g+h)(1/4) 8.) (h-g)(x) 9.) (f.g) x 10. (f.g) (1) 11.) (g.h) 12.) (h.g)

Solution

given,

f(x)=x2-9,g(x)=2x,h(x)=x-3.

We need to find out following values.

1.) f(3)

To find f(3) we have to substitute x with 3 in funtion f(x)

i.e., (3)^2-9=9-9=0

Therefore, f(3)=0

2.)g(3)

To find g(3) we have to substitute x with 3 in funtion g(x)

i.e.,2(3)=6

Therefore, g(3)=6

3.)h(6)

  To find h(6) we have to substitute x with 6 in funtion h(x)

i.e.,6-3=3

Therefore, h(6)=3

4.)(f+g)x

To find (f+g)x we have to add functions f(x) and g(x)

i.e.,x2-9+2x

Therefore, (f+g)x=x2+2x-9

5.)(f+g)3

From 4th problem (f+g)x=x2+2x-9

substitute x with 3 den we get (f+g)3

i.e.,3^2+2(3)-9=6

Therefore, (f+g)3=6

6.)(f-h)(-3)

Similarly subtract function f(x) and h(x) then substitute x with -3

i.e.,x2-9-(x-3)=x2-9-x+3=x2-x-6

(f-h)(-3)=(-3)^2-(-3)-6=6

Therefore, (f-h)(-3)=6

7.)(g+h)(1/4)

   Similarly add functions g(x) and h(x) then substitute x with 1/4

   i.e.,2x+x-3=3x-3

   (g+h)(1/4)=3(1/4)-3=(-9/4)

   Therefore, (g+h)(1/4)=(-9/4)

8.)(h-g)(x)

   Subtract function h(x) and g(x)

   i.e.,x-3-(2x)=x-3-2x=-x-3

   Therefore (h-g)(x)=-x-3

9.)(f.g)x

Multiply function f(x) and g(x)

   i.e.,(x2-9)(2x)=2x3-18x

   Therefore, (f.g)x=2x3-18x

10.)(f.g)(1)

   From problem.9 we got (f.g)x=2x3-18x

By substituting x with 1 we get,

(f.g)(1)=2(1)-18(1)=2-18=-16

   Therefore, (f.g)(1)=-16

11.)(g.h)x

Multiply functions g(x) and h(x) we get,

   (2x)(x-3)=2x2-6x

   Therefore, (g.h)x=2x2-6x

12.)(h.g)x

   Multiply functions h(x) and g(x) we get,

   (x-3)(2x)=2x2-6x

   Therefore,(h.g)x=2x2-6x