Example 1 · level 1
If f(x) = 3x² + 5x + 8, find f(−3).
Show solution
- 3 × (−3)² = 27; 5 × (−3) = −15.
- f(−3) = 27 − 15 + 8 = 20.
Answer: 20
CLASS 11 MATHS · RELATIONS AND FUNCTIONS
Function values, composition and counting relations
Substitute to find f(a). For f(g(x)), work from the inside out. If n(A) = m and n(B) = n, A × B has mn pairs, so there are 2^(mn) relations from A to B.
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Worked examples
Example 2 · level 2
If f(x) = 5x − 4 and g(x) = x², find g(f(4)).
Show solution
- f(4) = 16.
- g(16) = 256.
Answer: 256
Example 3 · level 3
A has 3 elements and B has 3 elements. How many relations are there from A to B?
Show solution
- n(A × B) = 9.
- Number of relations = 2⁹ = 512.
Answer: 512