The inverse of the function f(x) = 2x-9 is ________.

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Accepted Answer

{"content":[{"content":[{"marks":[{"type":"bold"}],"text":"Step 1 (Setup inverse equation):","type":"text"},{"text":" Let ","type":"text"},{"attrs":{"latex":"y = f(x)"},"type":"math_inline"},{"text":":","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"y = 2x - 9"},"type":"math_block"},{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 2 (Solve for x in terms of y):","type":"text"},{"type":"text","text":" We isolate the variable "},{"attrs":{"latex":"x"},"type":"math_inline"},{"text":":","type":"text"}]},{"type":"math_block","attrs":{"latex":"2x = y + 9"}},{"attrs":{"latex":"x = \frac{y + 9}{2}"},"type":"math_block"},{"content":[{"text":"Step 3 (Formulate Inverse Function):","type":"text","marks":[{"type":"bold"}]},{"text":" We replace ","type":"text"},{"attrs":{"latex":"y"},"type":"math_inline"},{"type":"text","text":" with "},{"attrs":{"latex":"x"},"type":"math_inline"},{"text":" to obtain the inverse function ","type":"text"},{"attrs":{"latex":"f^{-1}(x)"},"type":"math_inline"},{"text":":","type":"text"}],"type":"paragraph"},{"type":"math_block","attrs":{"latex":"f^{-1}(x) = \frac{x + 9}{2}"}},{"content":[{"text":"Step 4 (Conclusion):","type":"text","marks":[{"type":"bold"}]},{"text":" The inverse of the function is exactly ","type":"text"},{"marks":[{"type":"code"}],"text":"(x+9)/2","type":"text"},{"type":"text","text":"."}],"type":"paragraph"}],"type":"doc"}

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