AlgebraVery hardComposition of a linear function with itself
Algebra practice question
The function g is defined by g(x) = −2x + c, where c is a constant. If g(g(1)) = 3, what is the value of c?
Answer: 1
g(1) = −2 + c. Then g(−2 + c) = −2(−2 + c) + c = 4 − c. Setting 4 − c = 3 gives c = 1.
Common wrong answers
- If you answered 3
- 3 is the given output, not c.
- If you answered 5
- 5 comes from solving g(1) = 3 alone, ignoring the outer g.
- If you answered -1
- −1 comes from a sign slip in −2(−2 + c).
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