Question

Two functions are defined for x ∈ R as f(x) = x2 and g(x) = x2 + 4x − 1. (i) Find a and b so that g(x) = f(x + a) + b.

Answer 1

Hope u like my process
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$= > f(x) = \bf \: {x}^{2} \\ \\ = > f(x + a) = \bf {(x + a)}^{2} = {x}^{2} + {a}^{2} + 2ax \\ \\ = > g(x) =\bf f(x + a) + b \\ \\ or. \: \: \bf {x}^{2} + 4x - 1 = {x}^{2} + {a}^{2} + 2ax + b \\ \\ \bf \underline{so.....} \\ \\ = > 2ax = 4x \\ \\ = > \bf \: x = \frac{4x}{2x} = \: \underline{2 } \\ \\ \\ \bf \underline{and.....} \\ \\ = > {a}^{2} + b = - 1 \\ \\ or. \: \: b = - 1 - {a}^{2} = - 1 - {2}^{2} \\ \\ or. \: \: \bf \: \: b = \underline{ - 5 }$
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