Back to: Further Mathematics SS1

**COMPOSITE MAPPING:**

A mapping is composite when the co- domain of the first mapping is the domain of the second mapping.

Consider the mapping f;X→ Z and g: Z→Y

**SOLUTION**:

(a) F(-3) + F(4) = -5 + 9 = 4

(b) F(2) + F(-5) = 5 +(-10) = -5

(c) G[f(-3)] = g(-5) = -10

(d) G[f(-3)] + g[f(4)] = g(-5) + g(9) = -10 + 18 = 8

Example 2: The functions f and g on the set of real numbers are defined by f(x) = 3x-1 and g(x) = 5x+2 respectively. Find (a) F [g(x)] (b) g [f(x)] (c) 2f(x) – g(x)

**SOLUTION:**

(a) f[g(x)] = f(5x+2), 5x+2 will represent x in f(x)

f ( 5x +2) = 3 (5x+2) – 1

= 15x +5

(b) g [f(x)] = g( 3x-1)

= g(3x-1) = 5(3x-1) + 2

= 15x -5 +2

= 15x-3

(c) 2f(x) – g(x) = 2(3x-1) – (5x+2)

= 6x -2 -5x -2

= x-4

**INVERSE MAPPING**:

A function has an inverse if it’s both one- one and onto. Consider the function f(x) = __x-3__ on the set p={ -1, 5, 9} into set

Q ={ -2,1,3 }

Example: The function f is defined on the ser of real numbers by f(x) = __2x-1, (__x≠-2/3)

3x +2

Determine (a) f^{-1}(x) (b) f^{-1} (-2) (c) determine the largest domain of f^{-1}(x)

**SOLUTION**:

(a) F(x) = __2x-1__

3x+2

f^{-1}(x), y = __2x-1__

3x+2

(3x+2) y = 2x-1

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