FIND COMPOSITION OF TWO FUNCTIONS

Example 1 :

Find f o g, if f(x) = x and g(x) = 3x².

Solution :

f o g = f[g(x)]

= f[3x²]

= 3x²

Example 2 :

If f(x) = 2x - 5 and g(x) = x + 2 find f o g.

Solution :

f o g = f[g(x)]

= f[x + 2]

= 2(x + 2) - 5

= 2x + 4 - 5

= 2x - 1

Example 3 :

If f(x) = -3x + 4 and g(x) = x² find g o f. 

Solution :

g o f = g[f(x)]

= g[-3x + 4]

= (-3x + 4)²

= (-3x)² + 2(-3x)(4) + 4²

= 9x² - 24x + 16

Example 4 :

If f(x) = 4x² + 2 and g(x) = √(x- 8) find f o g.

Solution :

f o g = f[g(x)]

= f[√(x- 8)]

= 4[√(x- 8)]² + 2

= 4(x- 8) + 2

= 4x - 32 + 2

= 4x - 30

Example 5 :

If f(x) = -9x + 4 and g(x) = x⁴, find g o f.

Solution :

g o f = g[f(x)]

= g[-9x + 4]

= (-9x + 4)⁴

Example 6 :

If f(x) = 2x + 1 and g(x) = x² - 2, then verify f o g = g o f.

Solution :

f o g :

= f[g(x)]

= f[x² - 2]

= 2(x² - 2) + 1

= 2x² - 4 + 1

= 2x² - 3 ----(1)

g o f :

= g[f(x)]

= g[2x + 1]

= (2x + 1)² - 2

= (2x)² + 2(2x)(1) + 1² - 2

= 4x² 4x + 1 - 2

= 4x² 4x - 1 ----(2)

From (1) and (2), we see that f o g ≠ g o f.

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