SAT Linear functions Practice Question 19 (Hard)

Math · AlgebraHard

The linear function $h$ satisfies $h(2x - 1) = 6x + 5$ for all values of $x$ . What is the value of $h(7)$ ?

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Answer: 29

Find the $x$ that makes the input equal 7: $2x - 1 = 7$ , so $x = 4$ . Then $h(7) = 6(4) + 5 = 29$ . (Equivalently, $h(t) = 3t + 8$ .)

Substituting 7 directly into $6x + 5$ gives 47, which is $h(13)$ , not $h(7)$ .

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