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{:[h(x)=3x-4],[g(x)=x^(2)-5x],[" Find "(h+g)(x)]:} {:[g(x)=x^(3)+4x],[h(x)=4x-4],[" Find "(5g-5h)(x)]:}

33)\newlineh(x)=3x−4g(x)=x2−5x Find (h+g)(x) \begin{array}{l} h(x)=3 x-4 \\ g(x)=x^{2}-5 x \\ \text { Find }(h+g)(x) \end{array} \newline44)\newlineg(x)=x3+4xh(x)=4x−4 Find (5g−5h)(x) \begin{array}{l} g(x)=x^{3}+4 x \\ h(x)=4 x-4 \\ \text { Find }(5 g-5 h)(x) \end{array}

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Q. 33)\newlineh(x)=3x−4g(x)=x2−5x Find (h+g)(x) \begin{array}{l} h(x)=3 x-4 \\ g(x)=x^{2}-5 x \\ \text { Find }(h+g)(x) \end{array} \newline44)\newlineg(x)=x3+4xh(x)=4x−4 Find (5g−5h)(x) \begin{array}{l} g(x)=x^{3}+4 x \\ h(x)=4 x-4 \\ \text { Find }(5 g-5 h)(x) \end{array}
  1. Identify Functions and Operations: Identify the given functions and the operations to be performed.\newlineWe have two pairs of functions and two different operations to perform on them:\newline11. h(x)=3x−4h(x) = 3x - 4 and g(x)=x2−5xg(x) = x^2 - 5x, we need to find (h+g)(x)(h + g)(x).\newline22. g(x)=x3+4xg(x) = x^3 + 4x and h(x)=4x−4h(x) = 4x - 4, we need to find (5g−5h)(x)(5g - 5h)(x).
  2. Find (h+g)(x)(h+g)(x): Find the expression for (h+g)(x)(h+g)(x).\newlineTo find (h+g)(x)(h + g)(x), we simply add the functions h(x)h(x) and g(x)g(x) together:\newline(h+g)(x)=h(x)+g(x)(h + g)(x) = h(x) + g(x)\newline=(3x−4)+(x2−5x)= (3x - 4) + (x^2 - 5x)\newlineCombine like terms:\newline=x2−2x−4= x^2 - 2x - 4
  3. Find (5g−5h)(x)(5g-5h)(x): Find the expression for (5g−5h)(x)(5g-5h)(x). To find (5g−5h)(x)(5g - 5h)(x), we multiply each function by 55 and then subtract 5h(x)5h(x) from 5g(x)5g(x): (5g−5h)(x)=5g(x)−5h(x)=5(x3+4x)−5(4x−4)(5g - 5h)(x) = 5g(x) - 5h(x) = 5(x^3 + 4x) - 5(4x - 4) Distribute the 55 into each term: =5x3+20x−(20x−20)= 5x^3 + 20x - (20x - 20) Combine like terms: =5x3+20= 5x^3 + 20

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