SOLUTION: Let f(x) = 2x, g(x) = x—5, and h(x)=x^2-1. Find each value. (1) (fh)(2) (2) (gh)(-2) (3) (f/h) (4) (h/g)(0) (5) (g/f)(x)

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Question 1201999: Let f(x) = 2x, g(x) = x—5, and h(x)=x^2-1. Find each value.
(1) (fh)(2)
(2) (gh)(-2)
(3) (f/h)
(4) (h/g)(0)
(5) (g/f)(x)
Found 3 solutions by josgarithmetic, math_tutor2020, ikleyn:
Answer by josgarithmetic(39625)   (Show Source): You can put this solution on YOUR website!
SIMPLE SUBSTITUTIONS!

Only helping with ONE of those.

(4)






Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Normally I would point out that the rule of this website is "one question per post".

However, these questions are fairly short so it's not the end of the world to have them all together like this.

====================================================================================

Problem 1

Method 1
f(x) = 2x
f(2) = 2*2
f(2) = 4
and
h(x) = x^2-1
h(2) = 2^2-1
h(2) = 4-1
h(2) = 3
those results lead to
(fh)(2) = f(2)*h(2)
(fh)(2) = 4*3
(fh)(2) = 12

Method 2
(fh)(x) = f(x)*h(x)
(fh)(x) = ( f(x) )*( h(x) )
(fh)(x) = ( 2x )*( x^2-1 )
(fh)(x) = 2x^3-2x
(fh)(2) = 2*2^3-2*2
(fh)(2) = 2*8-4
(fh)(2) = 16-4
(fh)(2) = 12


Answer: 12

=======================================================

Problem 2

Method 1
g(x) = x-5
g(-2) = -2-5
g(-2) = -7
and
h(x) = x^2-1
h(-2) = (-2)^2-1
h(-2) = 4-1
h(-2) = 3
so,
(gh)(-2) = g(-2)*h(-2)
(gh)(-2) = -7*3
(gh)(-2) = -21

Method 2
(gh)(x) = g(x)*h(x)
(gh)(x) = ( g(x) ) * ( h(x) )
(gh)(x) = ( x-5 ) * ( x^2-1 )
(gh)(x) = x( x^2-1 ) - 5( x^2-1 )
(gh)(x) = x^3-x -5x^2+5
(gh)(x) = x^3-5x^2-x+5
(gh)(-2) = (-2)^3-5(-2)^2-(-2)+5
(gh)(-2) = -8-5*(4)+2+5
(gh)(-2) = -8-20+2+5
(gh)(-2) = -21


Answer: -21

=======================================================

Problem 3

f(x) = 2x
h(x) = x^2 - 1
(f/h) = f(x)/h(x)
(f/h) = ( f(x) )/( h(x) )
(f/h) = (2x)/(x^2-1)


Answer: (2x)/(x^2-1)

=======================================================

Problem 4

Method 1
h(x) = x^2-1
h(0) = 0^2-1
h(0) = 0-1
h(0) = -1
and
g(x) = x-5
g(0) = 0-5
g(0) = -5
therefore,
(h/g)(x) = ( h(x) )/( g(x) )
(h/g)(0) = ( h(0) )/( g(0) )
(h/g)(0) = ( -1 )/( -5 )
(h/g)(0) = 1/5


Method 2
(h/g)(x) = ( h(x) )/( g(x) )
(h/g)(x) = ( x^2-1 )/( x-5 )
(h/g)(0) = ( 0^2-1 )/( 0-5 )
(h/g)(0) = ( -1 )/( -5 )
(h/g)(0) = 1/5


Answer: 1/5

=======================================================

Problem 5

g(x) = x-5
f(x) = 2x
(g/f)(x) = ( g(x) )/( f(x) )
(g/f)(x) = ( x-5 )/( 2x )

Answer: ( x-5 )/( 2x )
=======================================================

Summary:
  1. 12
  2. -21
  3. (2x)/(x^2-1)
  4. 1/5
  5. ( x-5 )/( 2x )
Answer by ikleyn(52852)   (Show Source): You can put this solution on YOUR website!
.

(1)  Calculate f(2) and h(2) separately, by substituting the value of x= 2 into the relevant formula.

     Then calculate the product of the obtained values.



(2)  Calculate g(-2) and h(-2) separately, by substituting the value of x= -2 into the relevant formula.

     Then calculate the product of the obtained values.



(4)  Calculate h(0) and g(0) separately, by substituting the value of x= -0 into the relevant formula.

     Then divide the obtained value h(0) by g(0).



In (3) and (5), it is impossible in principle to find the value, since the value of the input argument is not given.

---------------

I instructed you as much as possible. The rest is for your own exercises.

Happy calculations (!)



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