suppose f and g are continuous functions such that g(2) = 5 and lim_{x→2}3f(x)+f(x)g(x) = 24. find f(2).
suppose f and g are continuous functions such that g(2) = 5 and lim_{x→2}3f(x)+f(x)g(x) = 24. find f(2).
Answer
Explanation:
Step1: Use continuity property
Since (f) and (g) are continuous functions, (\lim_{x\rightarrow 2}[3f(x)+f(x)g(x)] = 3f(2)+f(2)g(2)).
Step2: Substitute known values
We know (g(2) = 5) and (\lim_{x\rightarrow 2}[3f(x)+f(x)g(x)]=24). So (3f(2)+f(2)\times5 = 24).
Step3: Combine like - terms
Factor out (f(2)) on the left - hand side: (f(2)(3 + 5)=24), which simplifies to (8f(2)=24).
Step4: Solve for (f(2))
Divide both sides by 8: (f(2)=\frac{24}{8}=3).
Answer:
3