find an expression for the indicated function if ( f(x)=3x - 1 ), ( g(x)=-3x^{2} ), and ( h(x)=4 + x^{2} )…

find an expression for the indicated function if ( f(x)=3x - 1 ), ( g(x)=-3x^{2} ), and ( h(x)=4 + x^{2} ). show your work.\n1. ( (f + h)(x) )\n2. ( (g + h)(x) )\n3. ( (h - g)(x) )\n4. ( (g - f)(x) )\n5. ( (gh)(x) )\n6. ( left(\frac{f}{g}\right)(x) )\n7. ( (f + g)(x) )\n8. ( (f - h)(x) )\n9. ( (fg)(x) )\n10. ( left(\frac{h}{f}\right)(x) )

find an expression for the indicated function if ( f(x)=3x - 1 ), ( g(x)=-3x^{2} ), and ( h(x)=4 + x^{2} ). show your work.\n1. ( (f + h)(x) )\n2. ( (g + h)(x) )\n3. ( (h - g)(x) )\n4. ( (g - f)(x) )\n5. ( (gh)(x) )\n6. ( left(\frac{f}{g}\right)(x) )\n7. ( (f + g)(x) )\n8. ( (f - h)(x) )\n9. ( (fg)(x) )\n10. ( left(\frac{h}{f}\right)(x) )

Answer

Explanation:

Step1: Recall the formula for function addition

For ((f + h)(x)), the formula is ((f + h)(x)=f(x)+h(x)). Given (f(x) = 3x - 1) and (h(x)=4 + x^{2}), substitute into the formula: ((f + h)(x)=(3x - 1)+(4 + x^{2}))

Step2: Simplify the expression

Combine like - terms: ((3x - 1)+(4 + x^{2})=x^{2}+3x+( - 1 + 4)=x^{2}+3x + 3)

Answer:

((f + h)(x)=x^{2}+3x + 3)