Tutor profile: Brianna T.
Solve f(g(x)) and g(f(x)). f(x)=5x+7 g(x)=9x^2
f(g(x)) means you put the g(x) function into the f(x) one. f(g(x))=5(9x^2)+7=45x^2+7. g(f(x))=9(5x+7)^2=9(5x+7)(5x+7). Foil the parenthesis before multiplying the 9 out. g(f(x))=9(25x^2+35x+35x+49)=9(25x^2+70x+49)=225x^2+630x+441.
Foil the (x+3)(x+10) which equals x^2+3x+10x+21. Simplify to x^2+13x+30. Now the function is 5x+14=x^2+13x+30. Combine like terms by subtracting 5x from both sides to get x^2+8x+30=14. Then subtract 14 from both sides to gt x^2+8x+16=0. Now factor x^2+8x+16=(x+4)(x+4)=0. To solve for x, you set each function equal to 0. In this problem both functions are the same so there is only one answer. x+4=0. Subtract 4 from both sides and x=-4.
Solve 24 = −4(−6x − 3).
First divide both sides by -4. This gives you -6 = -6x - 3. Add 3 to both sides: -3 = -6x. Now divide both sides by -6 so x = 1/2 = 0.5.
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