Math Problem Statement
Evaluate the following: a) Given a(x) = x^2 + 2x - 5, find a(x+3); b) Given b(x) = 5x + 3, find b(x^2 - 4)
Solution
Let's go through the two problems step by step.
Problem (a):
We are given and asked to find .
To do this, we substitute into the expression for .
Now, expand and simplify:
Substitute these back into the expression:
Simplify:
Problem (b):
We are given and asked to find .
To solve, we substitute into the expression for .
Now, expand:
Final Answers:
- (a)
- (b)
Would you like more details on these solutions or have any questions? Here are some related questions you could explore:
- What would be the result if instead?
- How would you solve for the same function ?
- What is the general method for evaluating for any function ?
- How can this process be applied to more complex functions, such as logarithmic or trigonometric functions?
- If were a quadratic function, how would you approach ?
Tip: When substituting into a function, always expand carefully and combine like terms to avoid errors.
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Math Problem Analysis
Mathematical Concepts
Algebra
Function Substitution
Quadratics
Formulas
a(x) = x^2 + 2x - 5
b(x) = 5x + 3
Theorems
Substitution in Algebraic Expressions
Suitable Grade Level
Grades 9-10