Exams › JEE Main › Maths

Given f(x) = 3x + 4, g(x) = x² + 1 for x >= 1 and 2x + 3 for x < 1, and h(x) = e^x for x >= 5, 2x² + 3x for 2 <= x < 5, and 5 - x for x < 2. Evaluate h(f(g(-2))).

1. 4
2. 1
3. e⁷
4. 13

Correct answer: 4

Solution

g(-2): since -2 < 1, g = 2(-2)+3 = -1. f(-1) = 3(-1)+4 = 1. h(1): since 1 < 2, use the branch 5 - x = 5 - 1 = 4. Therefore h(f(g(-2))) = 4.

Related JEE Main Maths questions

• Given f(x)=(x(x-p))/(q-p)+(x(x-q))/(p-q), where p≠ q, determine the value of f(p)+f(q).
• A real-valued function f(x) obeys the relation f(x-y)=f(x)f(y)-f(a-x)f(a+y), where a is a fixed constant, and f(0)=1. Then the value of f(2a-x) is
• The set of all real values of x for which the function f(x)=(3)/(4-x²)+log₁₀(x³-x) is defined is:
• A relation R is defined on the set of integers Z by the condition that (x,y) belongs to R exactly when x² + y² = 9. Which statement below is false?
• If f(x)=√(1+x²), then which of the following statements is true?
• For the function f(x)=√(x-√(1-x²)), what is its domain?

⚔️ Practice JEE Main Maths free + battle 1v1 →