8. Given $f(x) = x^2 + 3x - 5$ Express $f(2x - 1)$ in the form $ax^2 + bx + c$ 9. The function f is such that $f(x) = kx + 3$ The function g is such that $g(x) = 2x - 4$ Given that $gf(2) = 34$ work out the value of k 10. For all values of x, $f(x) = x^2 + 4$ $g(x) = x - 9$ Solve $fg(x) = gf(x)$
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To do this, we substitute $(2x - 1)$ for $x$ in the expression for $f(x)$. $f(2x - 1) = (2x - 1)^2 + 3(2x - 1) - 5$ Step 2: Expand the terms. $(2x - 1)^2 = (2x)^2 - 2(2x)(1) + (-1)^2 = 4x^2 - 4x + 1$ $3(2x - 1) = 6x - 3$ Step 3: Substitute the expanded terms Show more…
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In Exercises $1-8$, compute each expression, given that the functions $f, g, h, k,$ and $m$ are defined as follows: $$ \begin{array}{ll} f(x)=2 x-1 & k(x)=2, \text { for all } x \\ g(x)=x^{2}-3 x-6 & m(x)=x^{2}-9 \\ h(x)=x^{3} \end{array} $$ (a) $(f k)(x)$ (b) $(k f)(x)$ (c) $(f k)(1)-(k f)(2)$
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