## EVALUATING THE VALUE OF COMPOSITION FUNCTION FROM THE GIVEN FUNCTIONS

Evaluating the Value of Composition Function from the Given Functions :

Here we are going to see, how to evaluate the indicated value of composition functions from the table.

## Evaluating the Value of Composition Function from the Given Functions Examples

Question 1 :

Evaluate the indicated expression assuming that f(x) = √x, g(x) = (x + 1)/(x + 2) , h(x) = |x − 1|.

(i)  (f ◦ g)(4) (ii)  (f ◦ g)(5)  (iii)  (g ◦ f)(4)  (iv)  (g ◦ f)(5)

(v)  (f ◦ g ◦ h)(0)  (vi)  (h ◦ g ◦ f)(0)

Solution :

(f ◦ g)(4)  =  f[g(4)]  ---(1)

To evaluate the value of g(4), we have to apply the value 4 instead of x in the function g(x).

g(x)  =  (x + 1)/(x + 2)

g(4)  =  (4 + 1)/(4 + 2)  =  5/6

By applying the value of g(4) in (1), we get

=  f(5/6)

f(x)  =  √x

f(5/6)  =  √(5/6)

Hence the value of (f ◦ g)(4) is √(5/6).

(ii)  (f ◦ g)(5)

Solution :

(f ◦ g)(5)  =  f[g(5)]  ---(1)

To evaluate the value of g(5), we have to apply the value 4 instead of x in the function g(x).

g(x)  =  (x + 1)/(x + 2)

g(5)  =  (5 + 1)/(5 + 2)  =  6/7

By applying the value of g(5) in (1), we get

=  f(6/7)

f(x)  =  √x

f(6/7)  =  √(6/7)

Hence the value of (f ◦ g)(5) is √(6/7).

(iii)  (g ◦ f)(4)

Solution :

(g ◦ f)(4)  =  g[f(4)]  ----(1)

f(4)  =  √4  =  2

By applying the value of f(4) in (1), we get

=  g(2)

g(x)  =  (x + 1)/(x + 2)

g(2)  =  (2+1)/(2+2)

g(2)  =  3/4

Hence the value of (g ◦ f)(4) is 3/4.

(iv)  (g ◦ f)(5)

Solution :

(g ◦ f)(5)  =  g[f(5)]  ---(1)

f(x) = √x ==>  f(5)  =  √5

By applying the value of f(5) in (1), we get

=  g[√5]

g(x) = (√5 + 1)/(√5 + 2)

Hence the value of (g ◦ f)(5) is (√5 + 1)/(√5 + 2).

(v)  (f ◦ g ◦ h)(0)

Solution :

(f ◦ g ◦ h)(0)  =  (f ◦ g) [h(0)]  ----(1)

h(x) = |x − 1|

h(0) = |0 − 1|  =  1

By applying the value of h(0) in (1), we get

=  (f ◦ g) (1)

=  f [g(1)]  ----(2)

g(x) = (x + 1)/(x + 2)

g(1) = (1 + 1)/(1 + 2)  =  2/3

By applying the value of g(1) in (2), we get

=  f[2/3]

f(x) = √(2/3)

Hence the value of (f ◦ g ◦ h)(0) is √(2/3).

(vi)  (h ◦ g ◦ f)(0)

(h ◦ g ◦ f)(0)  =  (h ◦ g) [f(0)]  ----(1)

f(x)  = √x

f(0) = √0  =  0

By applying the value of f(0) in (1), we get

=  (h ◦ g) (0)

=  h [g(0)]  ----(2)

g(x) = (x + 1)/(x + 2)

g(0) = (0 + 1)/(0 + 2)  =  1/2

By applying the value of g(0) in (2), we get

=  h[2/3]

h(x) = |x − 1|

h(2/3) = |(2/3) − 1|

h(2/3) =  1/3

Hence the value of (h ◦ g ◦ f)(0) is (1/3).

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