Arbitrary-scale super-resolution (ASSR) aims to learn a single model for image super-resolution at arbitrary magnifying scales. Existing ASSR networks typically comprise an off-the-shelf scale-agnostic feature extractor and an arbitrary scale upsampler. These feature extractors often use fixed network architectures to address different ASSR inference tasks, each of which is characterized by an input image and an upsampling scale. However, this overlooks the difficulty variance of super-resolution on different inference scenarios, where simple images or small SR scales could be resolved with less computational effort than difficult images or large SR scales. To tackle this difficulty variability, in this paper, we propose a Task-Aware Dynamic Transformer (TADT) as an input-adaptive feature extractor for efficient image ASSR. Our TADT consists of a multi-scale feature extraction backbone built upon groups of Multi-Scale Transformer Blocks (MSTBs) and a Task-Aware Routing Controller (TARC). The TARC predicts the inference paths within feature extraction backbone, specifically selecting MSTBs based on the input images and SR scales. The prediction of inference path is guided by a new loss function to trade-off the SR accuracy and efficiency. Experiments demonstrate that, when working with three popular arbitrary-scale upsamplers, our TADT achieves state-of-the-art ASSR performance when compared with mainstream feature extractors, but with relatively fewer computational costs. The code is available at unmapped: uri https://github.com/Tillyhere/TADT.