The inverse of the function f(x)=2x-3 is ________.

Question

Accepted Answer

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

Guide / Hint

Solution