Let ƒ(x)=-3x+4 and g(x)=-x 2 +4x+1. Find each of the following. Simplify if necessary. ƒ(3t-2)

Evaluate F of 16 minus five for the function given below our functions F of X equal to negative 14 X plus 29. Now, what we can do first is we notice here we have f of 16 -5. Normally our form would be F of X 60 minus five. This implies our X is actually equal to 60 -5. We know this, we can plug in that for X and our equation F of 60 -5, It's equal to negative 14 times 16 - plus 29. Now we can go ahead and simplify Pay the times 16. That's when it's a negative 80 40. May the 14 times 8-5 is positive 70 And we bring down our 29 Simplified and more 84 T plus 99 we can't vilify any farther. So I answer native 80 40 plus 99 corresponds with answer D okay. I hope to help you solve the problem. Thanks for watching. Goodbye.

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1:20 minutes

Problem 66

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x²+4x+1. Find each of the following. Simplify if necessary. ƒ(3t-2)

Verified step by step guidance

Identify the given functions: $f(x) = -3x + 4$ and $g(x) = -x^{2} + 4x + 1$.

Focus on the function $f(x)$ since the problem asks for $f(3t - 2)$, which means we will substitute $x$ in $f(x)$ with the expression \$3t - 2$.

Write the substitution explicitly: $f(3t - 2) = -3(3t - 2) + 4$.

Apply the distributive property to multiply $-3$ by each term inside the parentheses: $-3 \times 3t$ and $-3 \times (-2)$.

Simplify the expression by combining like terms after distribution, but do not calculate the final numeric value.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Function Notation and Evaluation

Function notation, such as f(x), represents a rule that assigns each input x to an output f(x). Evaluating a function means substituting the given expression or value into the function's formula and simplifying the result.

Substitution of Algebraic Expressions

Substitution involves replacing the variable in a function with an algebraic expression instead of a single number. This requires careful distribution and simplification to correctly evaluate the function for the given input.

Simplifying Algebraic Expressions

Simplifying expressions means combining like terms and performing arithmetic operations to write the expression in its simplest form. This step ensures the final answer is clear and concise.

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