Question 2.7.1: If f(x)=3x-2 and g(x)=x³, find (f+g)(2),(f-g)(2),(fg)(2), an......
If f(x)=3x-2 and g(x)=x³, find (f+g)(2),(f-g)(2),(fg)(2), and (f/g)(2)
f(x)=3x-2
g(x)=x³
Step 1:
Find (f+g)(2) To find (f+g)(2), we need to add the values of f(2) and g(2). First, we find f(2) by substituting 2 into the function f(x): f(2) = 3(2) - 2 = 4 Next, we find g(2) by substituting 2 into the function g(x): g(2) = 2^3 = 8 Now, we can find (f+g)(2) by adding the values of f(2) and g(2): (f+g)(2) = f(2) + g(2) = 4 + 8 = 12
Step 2:
Find (f-g)(2) To find (f-g)(2), we need to subtract the values of f(2) and g(2). Using the values we found earlier, we have: (f-g)(2) = f(2) - g(2) = 4 - 8 = -4
Step 3:
Find (f*g)(2) To find (f*g)(2), we need to multiply the values of f(2) and g(2). Again, using the values we found earlier, we have: (fg)(2) = f(2) g(2) = 4 * 8 = 32
Step 4:
Find (f/g)(2) To find (f/g)(2), we need to divide the values of f(2) by g(2). Once again, using the values we found earlier, we have: (f/g)(2) = f(2) / g(2) = 4 / 8 = 1/2
Final Answer
\begin{aligned}&\text {Since} f(2)=3(2)-2=4 \text {and} g(2)=2^3=8, \text {we have}\\&(f+g)(2) =f(2)+g(2)=4+8=12 \\&(f-g)(2) =f(2)-g(2)=4-8=-4 \\&(f g)(2) =f(2) g(2)=(4)(8)=32 \\&\left(\frac{f}{g}\right)(2) =\frac{f(2)}{g(2)}=\frac{4}{8}=\frac{1}{2} .\end{aligned}
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